10
110
(K10a
100
)
A knot diagram
1
Linearized knot diagam
8 6 1 9 3 10 2 4 7 5
Solving Sequence
6,10 3,7
2 8 5 1 9 4
c
6
c
2
c
7
c
5
c
10
c
9
c
4
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.94814 × 10
60
u
50
+ 1.33577 × 10
61
u
49
+ ··· + 7.13614 × 10
60
b + 1.16812 × 10
61
,
4.97115 × 10
60
u
50
− 4.93286 × 10
59
u
49
+ ··· + 7.13614 × 10
60
a + 1.37929 × 10
62
, u
51
− 3u
50
+ ··· − 3u + 1i
I
u
2
= h−u
9
+ 3u
8
− 8u
7
+ 11u
6
− 14u
5
+ 10u
4
− 9u
3
+ 5u
2
+ b − 4u + 1,
− 2u
9
+ 4u
8
− 12u
7
+ 12u
6
− 20u
5
+ 10u
4
− 17u
3
+ 3u
2
+ a − 7u − 1,
u
10
− 2u
9
+ 6u
8
− 6u
7
+ 10u
6
− 5u
5
+ 9u
4
− 2u
3
+ 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 61 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−3.95×10
60
u
50
+1.34×10
61
u
49
+· · ·+7.14×10
60
b+1.17×10
61
, 4.97×
10
60
u
50
−4.93×10
59
u
49
+· · ·+7.14×10
60
a+1.38×10
62
, u
51
−3u
50
+· · ·−3u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−0.696616u
50
+ 0.0691250u
49
+ ··· + 26.3979u − 19.3282
0.553261u
50
− 1.87184u
49
+ ··· + 6.93494u − 1.63690
a
7
=
1
u
2
a
2
=
−1.24988u
50
+ 1.94096u
49
+ ··· + 19.4629u − 17.6913
0.553261u
50
− 1.87184u
49
+ ··· + 6.93494u − 1.63690
a
8
=
5.62576u
50
− 16.6964u
49
+ ··· + 84.9147u − 14.4475
1.31452u
50
− 3.25740u
49
+ ··· + 7.88805u + 0.493476
a
5
=
−5.07269u
50
+ 14.7750u
49
+ ··· − 63.8914u + 8.27803
−0.685403u
50
+ 1.65384u
49
+ ··· − 3.62278u − 0.452805
a
1
=
2.36727u
50
− 7.12893u
49
+ ··· + 76.0899u − 9.67668
−1.36131u
50
+ 4.21987u
49
+ ··· − 3.74774u + 3.48147
a
9
=
u
u
3
+ u
a
4
=
−5.82333u
50
+ 16.7794u
49
+ ··· − 68.9333u + 8.68998
−1.34927u
50
+ 3.56133u
49
+ ··· − 8.65673u + 0.206715
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.603997u
50
− 6.94205u
49
+ ··· + 39.9158u − 23.3331
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
51
− u
50
+ ··· + 559u + 143
c
2
, c
5
u
51
+ 3u
50
+ ··· + 97u + 17
c
3
u
51
− 3u
50
+ ··· + 2441u − 1003
c
4
, c
8
u
51
− u
50
+ ··· + 20u + 23
c
6
, c
9
u
51
− 3u
50
+ ··· − 3u + 1
c
10
u
51
+ u
50
+ ··· + 118u + 47
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
51
+ 41y
50
+ ··· − 137683y −20449
c
2
, c
5
y
51
+ 33y
50
+ ··· − 4701y −289
c
3
y
51
− 23y
50
+ ··· + 17745737y −1006009
c
4
, c
8
y
51
− 35y
50
+ ··· + 3022y −529
c
6
, c
9
y
51
+ 27y
50
+ ··· − 45y −1
c
10
y
51
− 9y
50
+ ··· + 9976y −2209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994943 + 0.185745I
a = 0.422541 − 1.311700I
b = 0.266229 − 1.334950I
−5.72149 − 2.82797I −6.95847 + 2.49384I
u = −0.994943 − 0.185745I
a = 0.422541 + 1.311700I
b = 0.266229 + 1.334950I
−5.72149 + 2.82797I −6.95847 − 2.49384I
u = 0.390188 + 0.947913I
a = −1.03830 − 1.40939I
b = 0.516208 − 1.186450I
0.72717 − 4.12473I 0.68433 + 2.44113I
u = 0.390188 − 0.947913I
a = −1.03830 + 1.40939I
b = 0.516208 + 1.186450I
0.72717 + 4.12473I 0.68433 − 2.44113I
u = −0.375762 + 0.890024I
a = −0.426976 + 0.241699I
b = 1.350530 − 0.349643I
0.99311 + 1.57122I −7.65217 − 5.55090I
u = −0.375762 − 0.890024I
a = −0.426976 − 0.241699I
b = 1.350530 + 0.349643I
0.99311 − 1.57122I −7.65217 + 5.55090I
u = 0.019775 + 1.071160I
a = −0.261242 − 0.274009I
b = 0.863662 + 0.336843I
3.46242 + 0.95472I 4.42129 − 1.75327I
u = 0.019775 − 1.071160I
a = −0.261242 + 0.274009I
b = 0.863662 − 0.336843I
3.46242 − 0.95472I 4.42129 + 1.75327I
u = 0.420839 + 1.017200I
a = −1.97618 − 0.11378I
b = 0.108632 − 1.103460I
−6.80830 − 3.96373I −9.29905 + 4.39229I
u = 0.420839 − 1.017200I
a = −1.97618 + 0.11378I
b = 0.108632 + 1.103460I
−6.80830 + 3.96373I −9.29905 − 4.39229I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526532 + 0.993852I
a = 1.216580 + 0.601262I
b = −0.68843 + 1.24828I
−7.65143 − 1.97817I −7.82727 + 2.61940I
u = 0.526532 − 0.993852I
a = 1.216580 − 0.601262I
b = −0.68843 − 1.24828I
−7.65143 + 1.97817I −7.82727 − 2.61940I
u = 0.506288 + 0.633852I
a = −0.296136 − 0.899365I
b = −0.37733 − 1.57824I
−8.80240 − 2.26810I −9.50846 + 5.46846I
u = 0.506288 − 0.633852I
a = −0.296136 + 0.899365I
b = −0.37733 + 1.57824I
−8.80240 + 2.26810I −9.50846 − 5.46846I
u = 0.557126 + 1.094830I
a = 0.113684 + 0.264643I
b = −1.213990 − 0.101030I
−3.13564 − 8.43581I 0
u = 0.557126 − 1.094830I
a = 0.113684 − 0.264643I
b = −1.213990 + 0.101030I
−3.13564 + 8.43581I 0
u = −0.113572 + 1.239660I
a = 0.242019 + 0.693111I
b = −0.450396 + 0.753572I
−0.289715 + 0.727443I 0
u = −0.113572 − 1.239660I
a = 0.242019 − 0.693111I
b = −0.450396 − 0.753572I
−0.289715 − 0.727443I 0
u = −0.520426 + 1.134500I
a = 1.06013 − 1.60375I
b = −0.390004 − 1.272450I
−2.08580 + 7.78838I 0
u = −0.520426 − 1.134500I
a = 1.06013 + 1.60375I
b = −0.390004 + 1.272450I
−2.08580 − 7.78838I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332771 + 0.672789I
a = −0.20644 + 2.43715I
b = 0.02668 + 1.44197I
−8.06580 + 0.63479I −8.35698 + 2.72496I
u = 0.332771 − 0.672789I
a = −0.20644 − 2.43715I
b = 0.02668 − 1.44197I
−8.06580 − 0.63479I −8.35698 − 2.72496I
u = −0.314342 + 1.210610I
a = 0.219903 − 0.392050I
b = −0.672500 + 0.034322I
1.72349 + 3.73342I 0
u = −0.314342 − 1.210610I
a = 0.219903 + 0.392050I
b = −0.672500 − 0.034322I
1.72349 − 3.73342I 0
u = −0.741826 + 1.022810I
a = −0.261173 + 1.316850I
b = 0.149560 + 1.061710I
−1.24787 + 2.87055I 0
u = −0.741826 − 1.022810I
a = −0.261173 − 1.316850I
b = 0.149560 − 1.061710I
−1.24787 − 2.87055I 0
u = −0.724864
a = −0.327919
b = −0.557789
−2.02066 −3.93810
u = 0.098596 + 0.711899I
a = 1.069920 + 0.850725I
b = −0.054343 + 0.710997I
−0.177529 + 1.103040I −2.91668 − 3.58562I
u = 0.098596 − 0.711899I
a = 1.069920 − 0.850725I
b = −0.054343 − 0.710997I
−0.177529 − 1.103040I −2.91668 + 3.58562I
u = 0.657571 + 1.111660I
a = 0.137365 + 0.376163I
b = 0.663637 + 0.521850I
−1.42681 − 1.13458I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657571 − 1.111660I
a = 0.137365 − 0.376163I
b = 0.663637 − 0.521850I
−1.42681 + 1.13458I 0
u = 0.610559 + 0.310111I
a = 0.21593 + 1.41416I
b = −0.723237 − 0.300626I
−5.30063 + 3.74184I −6.50172 − 2.38693I
u = 0.610559 − 0.310111I
a = 0.21593 − 1.41416I
b = −0.723237 + 0.300626I
−5.30063 − 3.74184I −6.50172 + 2.38693I
u = −0.681382 + 0.037993I
a = 0.18190 + 2.70537I
b = −0.349930 + 1.034050I
−4.86621 − 3.30300I −8.47560 + 3.00422I
u = −0.681382 − 0.037993I
a = 0.18190 − 2.70537I
b = −0.349930 − 1.034050I
−4.86621 + 3.30300I −8.47560 − 3.00422I
u = −0.611419 + 1.218010I
a = −0.827531 + 0.976005I
b = 0.63737 + 1.37202I
−2.65938 + 8.52301I 0
u = −0.611419 − 1.218010I
a = −0.827531 − 0.976005I
b = 0.63737 − 1.37202I
−2.65938 − 8.52301I 0
u = 1.283370 + 0.473849I
a = −0.337325 − 1.255760I
b = −0.381442 − 1.278540I
−9.75856 + 7.66724I 0
u = 1.283370 − 0.473849I
a = −0.337325 + 1.255760I
b = −0.381442 + 1.278540I
−9.75856 − 7.66724I 0
u = −0.732019 + 1.169240I
a = 0.788213 − 0.967707I
b = −0.299489 − 0.952219I
−0.86031 + 3.69765I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.732019 − 1.169240I
a = 0.788213 + 0.967707I
b = −0.299489 + 0.952219I
−0.86031 − 3.69765I 0
u = 1.03951 + 0.98801I
a = −0.44530 − 1.37365I
b = 0.511570 − 0.950776I
−2.64694 − 5.68594I 0
u = 1.03951 − 0.98801I
a = −0.44530 + 1.37365I
b = 0.511570 + 0.950776I
−2.64694 + 5.68594I 0
u = 0.75895 + 1.26498I
a = 0.81447 + 1.23333I
b = −0.60063 + 1.36529I
−7.1442 − 14.7775I 0
u = 0.75895 − 1.26498I
a = 0.81447 − 1.23333I
b = −0.60063 − 1.36529I
−7.1442 + 14.7775I 0
u = 0.004627 + 0.461649I
a = 1.30111 + 0.61627I
b = 0.111178 + 0.551129I
−0.190582 + 1.119640I −2.80508 − 5.30984I
u = 0.004627 − 0.461649I
a = 1.30111 − 0.61627I
b = 0.111178 − 0.551129I
−0.190582 − 1.119640I −2.80508 + 5.30984I
u = −0.30097 + 1.62417I
a = 0.295438 − 0.306674I
b = −0.047348 − 0.927946I
−0.09818 + 2.57183I 0
u = −0.30097 − 1.62417I
a = 0.295438 + 0.306674I
b = −0.047348 + 0.927946I
−0.09818 − 2.57183I 0
u = 0.042401 + 0.263814I
a = −7.33865 + 1.88245I
b = −0.177299 + 0.708964I
−5.09251 − 3.48313I −7.71213 + 0.11617I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.042401 − 0.263814I
a = −7.33865 − 1.88245I
b = −0.177299 − 0.708964I
−5.09251 + 3.48313I −7.71213 − 0.11617I
10
II.
I
u
2
= h−u
9
+3u
8
+· · ·+b+1, −2u
9
+4u
8
+· · ·+a−1, u
10
−2u
9
+· · ·+5u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
2u
9
− 4u
8
+ 12u
7
− 12u
6
+ 20u
5
− 10u
4
+ 17u
3
− 3u
2
+ 7u + 1
u
9
− 3u
8
+ 8u
7
− 11u
6
+ 14u
5
− 10u
4
+ 9u
3
− 5u
2
+ 4u − 1
a
7
=
1
u
2
a
2
=
u
9
− u
8
+ 4u
7
− u
6
+ 6u
5
+ 8u
3
+ 2u
2
+ 3u + 2
u
9
− 3u
8
+ 8u
7
− 11u
6
+ 14u
5
− 10u
4
+ 9u
3
− 5u
2
+ 4u − 1
a
8
=
−2u
9
+ 5u
8
− 13u
7
+ 16u
6
− 21u
5
+ 16u
4
− 18u
3
+ 12u
2
− 8u + 4
u
9
− u
8
+ 3u
7
+ 2u
6
− u
5
+ 9u
4
− u
3
+ 8u
2
+ 4
a
5
=
u
9
− 4u
8
+ 10u
7
− 17u
6
+ 20u
5
− 19u
4
+ 13u
3
− 11u
2
+ 5u − 4
−2u
9
+ 3u
8
− 9u
7
+ 5u
6
− 10u
5
− u
4
− 8u
3
− 4u
2
− 3u − 3
a
1
=
−3u
9
+ 5u
8
− 15u
7
+ 10u
6
− 18u
5
− u
4
− 12u
3
− 8u
2
− 5u − 6
−3u
9
+ 6u
8
− 17u
7
+ 16u
6
− 24u
5
+ 9u
4
− 18u
3
+ 2u
2
− 8u − 1
a
9
=
u
u
3
+ u
a
4
=
2u
9
− 6u
8
+ 16u
7
− 23u
6
+ 30u
5
− 24u
4
+ 21u
3
− 12u
2
+ 8u − 4
−u
9
+ u
8
− 3u
7
− u
6
− u
5
− 5u
4
− 2u
3
− 5u
2
− u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
9
+ 2u
8
− 10u
7
− 4u
6
− 9u
5
− 12u
4
− 17u
3
− 7u
2
− 11u − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 5u
8
− 2u
7
+ 9u
6
− 5u
5
+ 10u
4
− 6u
3
+ 6u
2
− 2u + 1
c
2
u
10
+ 2u
9
+ 5u
8
+ 8u
7
+ 10u
6
+ 11u
5
+ 9u
4
+ 7u
3
+ 5u
2
+ 2u + 1
c
3
u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 4u
6
− u
5
− 4u
4
− 2u
3
+ 4u
2
+ 4u + 1
c
4
u
10
− 3u
8
− u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− u + 1
c
5
u
10
− 2u
9
+ 5u
8
− 8u
7
+ 10u
6
− 11u
5
+ 9u
4
− 7u
3
+ 5u
2
− 2u + 1
c
6
u
10
− 2u
9
+ 6u
8
− 6u
7
+ 10u
6
− 5u
5
+ 9u
4
− 2u
3
+ 5u
2
+ 1
c
7
u
10
+ 5u
8
+ 2u
7
+ 9u
6
+ 5u
5
+ 10u
4
+ 6u
3
+ 6u
2
+ 2u + 1
c
8
u
10
− 3u
8
+ u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
− 2u
2
+ u + 1
c
9
u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 10u
6
+ 5u
5
+ 9u
4
+ 2u
3
+ 5u
2
+ 1
c
10
u
10
+ 4u
7
+ u
5
+ 4u
4
− 4u
3
+ 5u
2
− u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
10
+ 10y
9
+ ··· + 8y + 1
c
2
, c
5
y
10
+ 6y
9
+ 13y
8
+ 10y
7
− 4y
6
− 9y
5
+ 5y
4
+ 17y
3
+ 15y
2
+ 6y + 1
c
3
y
10
− 2y
9
+ y
8
+ 7y
7
− 2y
6
+ 21y
5
+ 2y
4
− 20y
3
+ 24y
2
− 8y + 1
c
4
, c
8
y
10
− 6y
9
+ 13y
8
− 9y
7
− 10y
6
+ 23y
5
− 14y
4
− 3y
3
+ 10y
2
− 5y + 1
c
6
, c
9
y
10
+ 8y
9
+ ··· + 10y + 1
c
10
y
10
− 8y
7
+ 2y
6
+ 33y
5
+ 32y
4
+ 26y
3
+ 25y
2
+ 9y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257364 + 0.963884I
a = −0.451800 + 0.245327I
b = 1.002200 + 0.257851I
1.64272 − 1.01431I 1.027334 − 0.251330I
u = 0.257364 − 0.963884I
a = −0.451800 − 0.245327I
b = 1.002200 − 0.257851I
1.64272 + 1.01431I 1.027334 + 0.251330I
u = −0.423126 + 0.723833I
a = 2.53899 − 0.73422I
b = −0.381869 − 0.772776I
−4.89025 + 4.25923I −4.77549 − 8.60184I
u = −0.423126 − 0.723833I
a = 2.53899 + 0.73422I
b = −0.381869 + 0.772776I
−4.89025 − 4.25923I −4.77549 + 8.60184I
u = 0.844499 + 1.066090I
a = −0.59283 − 1.31422I
b = 0.381449 − 1.077890I
−1.18159 − 4.79064I −4.32006 + 6.72204I
u = 0.844499 − 1.066090I
a = −0.59283 + 1.31422I
b = 0.381449 + 1.077890I
−1.18159 + 4.79064I −4.32006 − 6.72204I
u = −0.091508 + 0.559363I
a = 1.45456 + 1.86280I
b = −0.16645 + 1.44928I
−7.81345 + 1.55721I −4.98634 − 3.60342I
u = −0.091508 − 0.559363I
a = 1.45456 − 1.86280I
b = −0.16645 − 1.44928I
−7.81345 − 1.55721I −4.98634 + 3.60342I
u = 0.41277 + 1.49491I
a = 0.051075 + 0.569145I
b = 0.164670 + 0.651622I
0.72803 − 2.02366I 1.55456 + 1.03859I
u = 0.41277 − 1.49491I
a = 0.051075 − 0.569145I
b = 0.164670 − 0.651622I
0.72803 + 2.02366I 1.55456 − 1.03859I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 5u
8
− 2u
7
+ 9u
6
− 5u
5
+ 10u
4
− 6u
3
+ 6u
2
− 2u + 1)
· (u
51
− u
50
+ ··· + 559u + 143)
c
2
(u
10
+ 2u
9
+ 5u
8
+ 8u
7
+ 10u
6
+ 11u
5
+ 9u
4
+ 7u
3
+ 5u
2
+ 2u + 1)
· (u
51
+ 3u
50
+ ··· + 97u + 17)
c
3
(u
10
+ 4u
9
+ 7u
8
+ 7u
7
+ 4u
6
− u
5
− 4u
4
− 2u
3
+ 4u
2
+ 4u + 1)
· (u
51
− 3u
50
+ ··· + 2441u − 1003)
c
4
(u
10
− 3u
8
− u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− u + 1)
· (u
51
− u
50
+ ··· + 20u + 23)
c
5
(u
10
− 2u
9
+ 5u
8
− 8u
7
+ 10u
6
− 11u
5
+ 9u
4
− 7u
3
+ 5u
2
− 2u + 1)
· (u
51
+ 3u
50
+ ··· + 97u + 17)
c
6
(u
10
− 2u
9
+ 6u
8
− 6u
7
+ 10u
6
− 5u
5
+ 9u
4
− 2u
3
+ 5u
2
+ 1)
· (u
51
− 3u
50
+ ··· − 3u + 1)
c
7
(u
10
+ 5u
8
+ 2u
7
+ 9u
6
+ 5u
5
+ 10u
4
+ 6u
3
+ 6u
2
+ 2u + 1)
· (u
51
− u
50
+ ··· + 559u + 143)
c
8
(u
10
− 3u
8
+ u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
− 2u
2
+ u + 1)
· (u
51
− u
50
+ ··· + 20u + 23)
c
9
(u
10
+ 2u
9
+ 6u
8
+ 6u
7
+ 10u
6
+ 5u
5
+ 9u
4
+ 2u
3
+ 5u
2
+ 1)
· (u
51
− 3u
50
+ ··· − 3u + 1)
c
10
(u
10
+ 4u
7
+ ··· − u + 1)(u
51
+ u
50
+ ··· + 118u + 47)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
10
+ 10y
9
+ ··· + 8y + 1)(y
51
+ 41y
50
+ ··· − 137683y −20449)
c
2
, c
5
(y
10
+ 6y
9
+ 13y
8
+ 10y
7
− 4y
6
− 9y
5
+ 5y
4
+ 17y
3
+ 15y
2
+ 6y + 1)
· (y
51
+ 33y
50
+ ··· − 4701y −289)
c
3
(y
10
− 2y
9
+ y
8
+ 7y
7
− 2y
6
+ 21y
5
+ 2y
4
− 20y
3
+ 24y
2
− 8y + 1)
· (y
51
− 23y
50
+ ··· + 17745737y −1006009)
c
4
, c
8
(y
10
− 6y
9
+ 13y
8
− 9y
7
− 10y
6
+ 23y
5
− 14y
4
− 3y
3
+ 10y
2
− 5y + 1)
· (y
51
− 35y
50
+ ··· + 3022y −529)
c
6
, c
9
(y
10
+ 8y
9
+ ··· + 10y + 1)(y
51
+ 27y
50
+ ··· − 45y −1)
c
10
(y
10
− 8y
7
+ 2y
6
+ 33y
5
+ 32y
4
+ 26y
3
+ 25y
2
+ 9y + 1)
· (y
51
− 9y
50
+ ··· + 9976y −2209)
16
